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‎tutorials/1_models-quick-fit.html

Lines changed: 34 additions & 34 deletions
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@@ -688,7 +688,7 @@ <h2>2) Fit a Polynomial model: Choose fitter wisely<a class="headerlink" href="#
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;$y_1$&#39;)
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</pre></div>
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<img alt="_images/3634bb8b4c277819f7ce4c233fc84552a8f897def45ba7df53cedd5578cf8fde.png" src="_images/3634bb8b4c277819f7ce4c233fc84552a8f897def45ba7df53cedd5578cf8fde.png" />
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<img alt="_images/2599989f34957c875699451791904b2274c11a2e2bc68012705be41fe1a092b1.png" src="_images/2599989f34957c875699451791904b2274c11a2e2bc68012705be41fe1a092b1.png" />
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<p>To fit this data let’s remember the three steps: model, fitter and perform fit.</p>
@@ -714,9 +714,9 @@ <h2>2) Fit a Polynomial model: Choose fitter wisely<a class="headerlink" href="#
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Model set size: 1
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Degree: 3
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Parameters:
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c0 c1 c2 c3
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------------------ ------------------ ------------------ ------------------
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-8.414565124986794 11.315131284061778 -5.936420715916029 1.0350472068170264
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c0 c1 c2 c3
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------------------ ----------------- ----------------- -----------------
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-9.539737981721931 13.13686821526471 -6.59469741384606 1.106942942692932
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</pre></div>
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@@ -749,9 +749,9 @@ <h2>2) Fit a Polynomial model: Choose fitter wisely<a class="headerlink" href="#
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Model set size: 1
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Degree: 3
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Parameters:
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c0 c1 c2 c3
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------------------- -------------------- ------------------ ------------------
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0.20564283089638824 -0.15716654941300878 -1.239243988919935 0.4355616696000767
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c0 c1 c2 c3
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------------------- ------------------- ------------------- -------------------
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0.05827388205687127 -0.9985633709289792 -0.5044587963099965 0.30779273029154025
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</pre></div>
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</div>
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</div>
@@ -786,7 +786,7 @@ <h3>Compare results<a class="headerlink" href="#compare-results" title="Link to
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with LinearLSQFitter: 1.7254506507627694
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with LinearLSQFitter: 1.8508835268899093
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</pre></div>
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</div>
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@@ -799,7 +799,7 @@ <h3>Compare results<a class="headerlink" href="#compare-results" title="Link to
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with SimplexLSQFitter: 4.580753153741815
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with SimplexLSQFitter: 5.074823984271411
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</pre></div>
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@@ -818,10 +818,10 @@ <h3>Compare results<a class="headerlink" href="#compare-results" title="Link to
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7ff08227ba10&gt;
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f5ef5539850&gt;
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</pre></div>
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</div>
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<img alt="_images/b2cb6953351ca9c5f39fbc468440cdd51731a2b59186590a4e26b1d805a046f3.png" src="_images/b2cb6953351ca9c5f39fbc468440cdd51731a2b59186590a4e26b1d805a046f3.png" />
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<img alt="_images/7a6733b3fb0ae20d77bdd6eb3754bced5da6de6dc31264045bde5643e73b2965.png" src="_images/7a6733b3fb0ae20d77bdd6eb3754bced5da6de6dc31264045bde5643e73b2965.png" />
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<p>Results are as espected, the fit performed with the linear fitter is better than the second, non linear one.</p>
@@ -858,7 +858,7 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;$y_2$&#39;)
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</pre></div>
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<img alt="_images/9424b3add19b739bc9cbfc66cf567663995d37f79f0e0ac2bab63e87ff87f7d1.png" src="_images/9424b3add19b739bc9cbfc66cf567663995d37f79f0e0ac2bab63e87ff87f7d1.png" />
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<img alt="_images/6dd81643931b491f78dfdc497c02ba5cd2a724d940ed81ad662329bd6911b94a.png" src="_images/6dd81643931b491f78dfdc497c02ba5cd2a724d940ed81ad662329bd6911b94a.png" />
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<p>Let’s do our three steps to make the fit we want. For this fit we’re going to use a non-linear fitter, <code class="docutils literal notranslate"><span class="pre">LevMarLSQFitter</span></code>, because the model we need (<code class="docutils literal notranslate"><span class="pre">Gaussian1D</span></code>) is non-linear in the parameters.</p>
@@ -883,9 +883,9 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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Outputs: (&#39;y&#39;,)
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Model set size: 1
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Parameters:
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amplitude mean stddev
887-
------------------ ------------------- ------------------
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10.161667885872756 0.16429784623682972 10.000409076033547
886+
amplitude mean stddev
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----------------- -------------------- -----------------
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9.995883804181737 -0.34004726579476496 10.17125839102595
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</pre></div>
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@@ -911,7 +911,7 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.05133544 0.06625433 0.06645726]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.05048654 0.06965048 0.06992814]
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</pre></div>
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@@ -932,9 +932,9 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 10.161667885872756 +\- 0.2265732649327809
936-
Mean: 0.16429784623682972 +\- 0.2573991704994828
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Standard Deviation: 10.000409076033547 +\- 0.2577930649461142
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 9.995883804181737 +\- 0.22469208943894217
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Mean: -0.34004726579476496 +\- 0.26391377689507484
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Standard Deviation: 10.17125839102595 +\- 0.2644392980327242
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</pre></div>
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
@@ -943,11 +943,11 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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&lt;&gt;:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:4: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:6: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3529/1659586526.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3540/1659586526.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&quot;Amplitude: {} +\- {}&quot;.format(best_fit_gauss.amplitude.value, np.sqrt(cov_diag[0]))
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/tmp/ipykernel_3529/1659586526.py:4: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3540/1659586526.py:4: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Mean: {} +\- {}&quot;.format(best_fit_gauss.mean.value, np.sqrt(cov_diag[1])))
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/tmp/ipykernel_3529/1659586526.py:6: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3540/1659586526.py:6: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&quot;Standard Deviation: {} +\- {}&quot;.format(
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</pre></div>
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@@ -978,7 +978,7 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[10.16166902 0.1642994 10.00040685]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 9.9958822 -0.34004602 10.17126165]
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</pre></div>
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@@ -992,9 +992,9 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 10.16166901860214 +\- 0.2180138118181192
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Mean: 0.1642993992949413 +\- 0.24767662180935193
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Standard Deviation: 10.00040684622568 +\- 0.24805566376335159
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 9.995882201165184 +\- 0.2183918959101891
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Mean: -0.34004601987526745 +\- 0.256517214073858
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Standard Deviation: 10.17126165173596 +\- 0.25702807522378746
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</pre></div>
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
@@ -1003,11 +1003,11 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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&lt;&gt;:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3529/2222327920.py:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3540/2222327920.py:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Amplitude: {} +\- {}&quot;.format(p_opt[0], np.sqrt(p_cov[0, 0])))
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/tmp/ipykernel_3529/2222327920.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3540/2222327920.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Mean: {} +\- {}&quot;.format(p_opt[1], np.sqrt(p_cov[1, 1])))
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/tmp/ipykernel_3529/2222327920.py:3: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Standard Deviation: {} +\- {}&quot;.format(p_opt[2], np.sqrt(p_cov[2, 2])))
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using astropy.modeling: 0.9258750059366527
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using astropy.modeling: 0.944715147396767
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using scipy: 0.9258750059343416
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using scipy: 0.9447151474018781
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7ff0821b5cd0&gt;
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f5ef4f971d0&gt;
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<img alt="_images/9d65948539694d6a9224f22edf286e6e920acf5805cb94eeeb84f92f19db8cf0.png" src="_images/9d65948539694d6a9224f22edf286e6e920acf5805cb94eeeb84f92f19db8cf0.png" />
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<img alt="_images/cde6f3c949fb75493dbcea1b87215794d4ac7fffa2fdea3f36b30e5948d61e9f.png" src="_images/cde6f3c949fb75493dbcea1b87215794d4ac7fffa2fdea3f36b30e5948d61e9f.png" />
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<p><strong>Conclusion:</strong> Choose the method most convenient for every case you need to fit. We recomend <code class="docutils literal notranslate"><span class="pre">astropy.modeling</span></code> because is easier to write the name of the function you want to fit than to remember the expression every time we want to use it. Also, <code class="docutils literal notranslate"><span class="pre">astropy.modeling</span></code> becomes useful with more complicated models like <a class="reference external" href="http://docs.astropy.org/en/stable/modeling/#compound-models">two gaussians</a> plus a <a class="reference external" href="http://docs.astropy.org/en/stable/modeling/#blackbody-radiation">black body</a>, but that is another tutorial.</p>
@@ -1109,7 +1109,7 @@ <h2>4) Exercise: Your turn to choose<a class="headerlink" href="#exercise-your-t
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;$y_3$&#39;)
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<img alt="_images/5224aeb98f66c2f8304a7ecdd3d93e75f3acdf064da194bc12dfc2cfbbe1e7e0.png" src="_images/5224aeb98f66c2f8304a7ecdd3d93e75f3acdf064da194bc12dfc2cfbbe1e7e0.png" />
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<img alt="_images/8aa54b9792fc13374e1ac574202e4a6427d221b9f0edd309906c5774fa208870.png" src="_images/8aa54b9792fc13374e1ac574202e4a6427d221b9f0edd309906c5774fa208870.png" />
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</section>

‎tutorials/2_user-defined-model.html

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@@ -952,7 +952,7 @@ <h3>Basic custom model<a class="headerlink" href="#basic-custom-model" title="Li
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<img alt="_images/24135eafbd14b54450eed59c1ae24f404f505b30373f968e7df2d50c45cdd5e1.png" src="_images/24135eafbd14b54450eed59c1ae24f404f505b30373f968e7df2d50c45cdd5e1.png" />
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<img alt="_images/703fa0868fbba6f599174299b5f84e97b670a253763ce8f965258dc2f560cd77.png" src="_images/703fa0868fbba6f599174299b5f84e97b670a253763ce8f965258dc2f560cd77.png" />
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<p>We can define a simple custom model by specifying which parameters we want to fit.</p>
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<img alt="_images/cd0876bf852b45f8811ad113532d37f94f41bc20b48b3ca59ab46cb5177059c6.png" src="_images/cd0876bf852b45f8811ad113532d37f94f41bc20b48b3ca59ab46cb5177059c6.png" />
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Outputs: (&#39;y&#39;,)
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a b c
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------------------ ------------------- ------------------
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a b c
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------------------ ------------------- ----------------
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0.9516741086904221 -2.0392833256485625 1.15307525374791
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>np.float64(0.9086643008789133)
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>np.float64(0.9168271560292492)
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<p>For the full custom model we can easily set the <strong>derivative of the function</strong>, which is used by different <a class="reference external" href="http://docs.astropy.org/en/stable/modeling/#id21">fitters</a>, for example the <code class="docutils literal notranslate"><span class="pre">LevMarLSQFitter()</span></code>.</p>
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Outputs: (&#39;y&#39;,)
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----------------- ------------------ ------------------ ------------------
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3.010622137988566 1.9989300570434283 3.9905960395565723 1.0039014197353062
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a b c d
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------------------ ------------------ ----------------- ------------------
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2.8859510397819435 1.9877027580241713 4.082655746288697 0.9908546289146978
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</pre></div>
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@@ -1144,7 +1144,7 @@ <h3>Full custom model<a class="headerlink" href="#full-custom-model" title="Link
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<div class="cell_output docutils container">
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>np.float64(2.618555709093496)
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>np.float64(2.822160801510391)
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@@ -1177,7 +1177,7 @@ <h3>Exercise<a class="headerlink" href="#id4" title="Link to this heading">#</a>
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<img alt="_images/d5efcd2189269486eef4f8676216c111d7a1c6daeebf90c8e7fe0efea475bd38.png" src="_images/d5efcd2189269486eef4f8676216c111d7a1c6daeebf90c8e7fe0efea475bd38.png" />
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<img alt="_images/67fdfbc60b77570e7297b92e6bf0c78e8c01e46c4f61f765b86fcc345488c03c.png" src="_images/67fdfbc60b77570e7297b92e6bf0c78e8c01e46c4f61f765b86fcc345488c03c.png" />
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</section>

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